## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The grating has $~~513~~$ lines per millimeter.
We can write an expression for the angles of the diffraction orders: $sin~\theta_m = \frac{m~\lambda}{d}$ We can find $d$: $sin~\theta_2 = \frac{(2)~\lambda}{d}$ $d = \frac{(2)~\lambda}{sin~\theta_2}$ $d = \frac{(2)(620\times 10^{-9}~m)}{sin~39.5^{\circ}}$ $d = 1.95\times 10^{-6}~m$ We can find the number of lines per millimeter: $N = \frac{1.0\times 10^{-3}~m}{1.95\times 10^{-6}~m}$ $N = 513$ The grating has $~~513~~$ lines per millimeter.